Method of predicting crop yield loss due to n-deficiency

ABSTRACT

A method for determining the yield loss of a crop using remote sensor data is described. The yield loss is determined using the reflectivity of light by the crop canopy measured from remote sensor data such as an aerial photograph that is digitized and spatially referenced to the field&#39;s longitude and latitude. Pixel values from the aerial photograph, expressed relative to pixel values from well fertilized areas of the field, are transformed to yield losses using a linear transformation that was developed using empirical data. A similar method is described to determine recommended nitrogen fertilization rates for the crop fields. The yield loss data is useful for nitrogen fertilization management, as it allows a producer of crops to weigh the expense of fertilization against the loss of revenue due to yield loss.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a Continuation-in-Part Application of Non-Provisional application Ser. No. 13/959,144 filed on Aug. 5, 2013, which is a Continuation-in-Part Application of Non-Provisional application Ser. No. 13/481,245 filed on May 25, 2012, now U.S. Pat. No. 8,520,891, which is a Divisional Application of Non-Provisional application Ser. No. 11/936,564 filed on Nov. 7, 2007, now U.S. Pat. No. 8,208,680, which claims priority from Provisional Application Ser. No. 60/857,242 filed on Nov. 7, 2006, all of which are hereby incorporated by reference in their entireties.

FUNDING OF RESEARCH

This work was supported by the U.S. Environmental Protection Agency contract number X-98756601-0. The U.S. government has certain rights in this invention.

FIELD

The present invention is directed generally to methods for determining the health and yield of a crop, using remote sensing data such as aerial photographs. In particular, the present invention provides a method of determining optimal nitrogen application rates as well as predicted losses in crop yield due to nitrogen deficiency.

BACKGROUND

Loss of nitrogen can result in economic loss in crop production systems due to nitrogen deficiency and yield limitation. Nitrogen is susceptible to loss from soils by a variety of mechanisms. The nitrate form of nitrogen is prone to loss by either leaching or denitrification when soils are wet. Nitrogen losses associated with wet soil conditions are common types of nitrogen loss from agricultural soils. The magnitude of nitrogen loss, and the process by which the nitrogen is lost, depends strongly on soil temperature and soil hydrology. Variations in soil temperature and hydrology within a field, due to differences in microclimate, can lead to substantial spatial variability in the amount of nitrogen that is lost within a given field.

When nitrogen loss occurs after the application of nitrogen fertilizer, a likely outcome, in the absence of any further intervention, is that the crop will suffer from nitrogen deficiency, resulting in substantial yield loss and subsequent economic loss. The yields of many crops, including corn, rice, wheat, and potatoes, dramatically increase in response to nitrogen applications throughout the vegetative stages of growth.

A traditional approach to avoiding losses in crop yield due to nitrogen deficiency is to apply an excess of nitrogen fertilizer at planting to compensate for anticipated nitrogen losses due to leaching or other mechanisms. An alternative and arguably more efficient approach to a single sizable application of nitrogen fertilizer near planting is the practice of applying a low nitrogen fertilizer rate at planting, which may be fully or partially corrected by an additional nitrogen application as needed in midseason. A corn producer, for example, may apply a low nitrogen rate near planting, and then apply additional nitrogen through a pivot irrigation system at growth stage V9 or later (Ritchie et al. 1993). Because the need for nitrogen is often spatially variable, accurate spatial diagnosis of nitrogen status can reduce the over-application of fertilizer, groundwater contamination, and can also increase nitrogen use efficiency, resulting in reduced operating costs. Thus, applying nitrogen to the growing crop, referred to in the art as rescue nitrogen application, is an effective way to respond to loss of fertilizer nitrogen.

Rescue nitrogen applications for corn and other crops are typically more expensive than primary nitrogen applications due to the height of the crops at the time the rescue nitrogen is applied, which usually create a need for specialized high-clearance equipment or aerial applications of nitrogen. The availability of equipment for high-clearance or aerial applications is often limited, meaning that it takes considerable effort on the part of a corn producer to arrange for these nitrogen applications. Balancing the cost and inconvenience of rescue nitrogen application against the economic impact of anticipated yield loss would help producers to make sound decisions about whether to proceed with rescue nitrogen applications.

Traditional technologies and methods for measuring leaching and denitrification losses of nitrogen are difficult and expensive, which limit a producer's ability to predict nitrogen loss and to utilize rescue nitrogen fertilization in order to minimize the potential yield loss for a particular field or section of a field. The soil may be periodically tested for nitrogen content at different depths and locations throughout the fields of a farm. Crop information may also be obtained using an apparatus in which the light with a wavelength related to crop nitrogen content is irradiated on a leaf blade of the crop and based on the reflectivity of the leaf at this wavelength of light; the leaf blade nitrogen content is measured with high precision. However, each of these techniques of monitoring soil and crop nitrogen content are highly localized. In order to determine the crop information accurately for the overall field, as well as to obtain an accurate mapping of the spatial variation of the crop information, numerous repeats of the minute measurements described above are required. Obtaining crop information in this manner is time-consuming, labor intensive, expensive, and may not supply the information in time for the farmer to apply rescue nitrogen effectively.

The increasing availability of commercial remote-sensing services tailored to the needs of agriculture offers new opportunities to develop and improve rescue nitrogen management strategies. Several studies have evaluated remote sensing techniques to determine corn nitrogen status during the growing season and have determined that the reflectance of corn near the 550 nm green visible band is significantly correlated with leaf nitrogen concentration or other variables related to crop nitrogen status, and therefore can be used to detect nitrogen deficiencies in crop canopy. Particularly, nitrogen-deficient corn reflects more visible light than nitrogen sufficient corn, which suggests that light reflectance can be quantitatively related to the amount of nitrogen stress experienced by the crop.

The specific relationship between crop reflectivity and nitrogen status has been developed to some extent, but no specific or general relationships for predicting nitrogen loss or yield loss from remotely sensed data have been developed. To date, this relationship has been determined by adding increasing quantities of nitrogen to a system that is nitrogen-limited. For application to nitrogen loss situations, it is more appropriate to define the relationship between color, nitrogen stress, and yield in the context of a fully fertilized crop that experiences a range of nitrogen losses. The resulting relationship between nitrogen stress (as measured by crop color) and yield loss most directly addresses the question that is most salient to the producer: does it make good business sense to apply rescue nitrogen fertilization to my nitrogen-stressed crops, or does the cost of fertilization outweigh the gain in crop yield?

Remote sensing using aerial and satellite photography as well as ground based sensors have been used to determine several parameters related to the successful cultivation of crops, including soil nutrient content, chlorophyll content of crop leaves, and nitrogen content of crop leaves. The factors measured using remote sensing are correlated with the overall health and nutrient status of the crops. In general, these methods rely on variations in the reflectivity of the soil or the crop canopy to selected wavelengths of light falling within the visible and the near-infrared spectrum. Soil nitrogen content is correlated with the soil's reflectivity of infrared light, and crop nitrogen content is associated with increased reflectivity of the leaves in the crop canopy to visible light. Although this increased reflectance of nitrogen-rich plant leaves may be most pronounced within the green wavelengths of the visible light spectrum, the reflectance of nitrogen-rich plant leaves in other colors such as blue or red may also be significantly correlated to crop health.

Most cameras used for the remote sensing of crops record a three spectral image combining either the near infrared, red, and green wavelengths or the red, green, and blue wavelengths. Remote sensing methodologies used for the determination of crop nitrogen status generally process the intensity of the colors contained in each pixel of a digital image of a field, and determines the variation in the intensity of each color. In order to minimize the confounding effects of spatial and temporal variations in camera angle, altitude, camera focal length, and ambient lighting, many remote sensing methods determine changes in pixel colors relative to the colors of other pixels in the field. By combining the relative intensity of green in each pixel with measured coordinates that determine the spatial distribution of the pixels, a relative greenness map may be developed.

Previous methods have used the relative greenness map to make determinations about the health of the crops, and in some cases may determine an optimal nitrogen fertilization rate that results in crops that are supplied with exactly the amount of supplemental nitrogen necessary to optimize crop health and yield. However, optimizing the growth and harvest of the crops is only half of the information necessary for a producer to manage the growth and care of crops. When managing the production of crops, the producer must constantly weigh the cost of additional nitrogen fertilization against the potential increase in revenue from the sale of the additional crop yield. To date, current field management methodologies that utilize remote sensing lack the capability to determine the impact of variations in the health and nutritional status of crop plants on the crop yield.

At the present time, there exists an unmet need to determine the impact of crop nutrient status on the resulting crop yield using remote sensing technology such as aerial photographs. The results of this method would make it possible for the producer to manage the nitrogen supplementation of the crops informed by the economic impact of any nitrogen deficiency on crop yield.

SUMMARY

The present disclosure provides a method for determining a crop yield loss due to nitrogen deficiency in at least one or more crop fields based on an analysis of at least one or more remote sensing images. In this aspect, the method includes obtaining the one or more remote sensing images of the at least one or more crop fields and assigning spatial coordinates to the at least one or more remote sensing images, represented by pixels or polygons comprised of aggregated pixels, from the at least one or more remote sensing images. The method also includes calculating a combination index value comprising at least two wavelengths at each pixel and selecting a reference index value from the combination index values. In addition, the method includes calculating a relative index value of each pixel in the at least one or more remote sensing images by dividing the combination index value by the reference index value and estimating a yield loss of each pixel from a function of the relative index values. A yield loss map may be constructed from a spatially referenced yield loss of each pixel and the yield loss includes a decrease in crop yield per acre of a crop.

In another aspect of the disclosure, a method of determining a nitrogen fertilization rate of a crop field at mid-season to ameliorate nitrogen deficiency using a spatially referenced map of relative index values (RI), wherein each RI comprises a combination index value at a location in a canopy of the crop field relative to a reference index value is provided. In this aspect, the method includes estimating an economically optimal nitrogen rate (EONR) corresponding to each RG of the spatially referenced map by substituting each RI into the equation EONR=C3×RI−C4, in which C3 and C4 are empirically derived constants. The method also includes mapping each EONR corresponding to each RI onto a spatially referenced EONR map; in which each EONR includes a recommended amount of nitrogen per unit area to be applied at mid-season in order to minimize a predicted crop yield loss due to nitrogen deficiency.

In another aspect of the disclosure, a method for determining a crop yield loss due to nitrogen deficiency in at least one or more crop fields based on an analysis of at least one or more remote sensing images is provided. In this aspect, the method includes obtaining the one or more remote sensing images of the at least one or more crop fields and assigning spatial coordinates to the at least one or more remote sensing images, represented by pixels or polygons comprised of aggregated pixels, from the at least one or more remote sensing images. The method also includes establishing a reference color value for a reflectivity of a color for the at least one or more remote sensing images; the color is selected from red, blue, green, red-edge, and infrared. In addition, the method includes calculating a relative color value of each pixel in the at least one or more remote sensing images by dividing a color value of each pixel by the reference color value, estimating a yield loss (YL) of each pixel by substituting the relative color value (RC) of each pixel into the formula YL=C1×RC−C2, in which C1 and C2 are empirically derived constants, and constructing a yield loss map from a spatially referenced yield loss of each pixel. The yield loss entails a decrease in crop yield per acre of a crop.

In another aspect of the disclosure, a method of determining the yield loss of a crop due to nitrogen deficiency based on a spatially referenced map that includes a plurality of spatial coordinates and corresponding relative color values within a crop field in provided. The method in this aspect includes estimating the yield loss (YL) of each spatial coordinate of the spatially referenced map by substituting each corresponding relative color value (RC) into the formula YL=C1×RC−C2, in which C1 and C2 are empirically-derived constants. The method further includes constructing a yield loss map from a spatially referenced YL of each spatial coordinate; the yield loss entails a decrease in crop yield per acre of a crop.

In yet another aspect of the disclosure, a method of determining a nitrogen fertilization rate of a crop field at mid-season to ameliorate nitrogen deficiency using a spatially referenced map of relative color values (RC). Each RC includes the reflectivity of a color of a light chosen from red, green, blue, red-edge, and infrared at a location in a canopy of the crop field relative to a reference RC. The method includes estimating an economically optimal nitrogen rate (EONR) corresponding to each RG of the spatially referenced map by substituting each RC into the equation EONR=C3×RC−C4 in which C3 and C4 are empirically derived constants. The method also includes mapping each EONR corresponding to each RC onto a spatially referenced EONR map. Each EONR comprises a recommended amount of nitrogen per unit area to be applied at midseason in order to minimize a predicted crop yield loss due to nitrogen deficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

The inventive method may be employed to predict crop (especially corn) yield loss for nitrogen-deficiency due to low nitrogen fertilization rate at planting but no nitrogen loss in mid-season (“nitrogen-stress-no-nitrogen-loss”), or due to nitrogen loss caused by wet weather or other factors following sufficient nitrogen fertilization early in the season (“nitrogen-loss”).

FIG. 1 is a flowchart illustration of the inventive method.

FIG. 2 illustrates the relationship between relative yield and relative green from individual fields.

FIG. 3 illustrates the relationship between relative yield and relative green from combined data across all seven fields.

FIG. 4 illustrates the relationship between yield loss and relative green from individual fields.

FIG. 5 illustrates the relationship between yield loss and relative green from combined data across seven fields.

FIG. 6 is a summary of the crop yield resulting from nitrogen fertilization management informed by an assessment of crop nitrogen deficiency using aerial photographic data.

FIG. 7 is a graph summarizing the correlation of crop yield loss as a function of relative blue value for a plurality of crop fields.

FIG. 8 is a graph summarizing the correlation of crop yield loss as a function of relative blue value for a plurality of crop fields.

FIG. 9 is a graph summarizing the correlation of crop yield loss as a function of relative index value for a combination index value of infrared and green for a plurality of crop fields.

Corresponding reference characters and labels indicate corresponding elements among the views of the drawings. The headings used in the figures should not be interpreted to limit the scope of the claims.

DETAILED DESCRIPTION

The present invention describes a method for determining nutrient deficiency and resulting crop yield loss using aerial photographs and positional data. In particular, the invention provides a method of determining yield loss due to nitrogen-deficiency using aerial photographs. In an aspect, the crop may be corn, rice, wheat, potatoes, grass, or cotton. In essence, the invention provides a method for estimating nitrogen deficiency in a field of crops, predicting the resulting loss of crop yield due to the nitrogen deficiency, and lastly providing information to help the producer to determine whether additional nitrogen fertilization would be economically profitable. A flowchart showing the steps comprising the inventive method is shown in FIG. 1.

After obtaining high-resolution digital aerial photographs of a field or fields of interest, spatial coordinates are assigned to the aerial image using the spatial coordinates of reference landmarks shown in the aerial photos. The aerial image is subdivided into one or more polygons. Within each polygon, the color intensity of each pixel is averaged to determine the mean pixel color intensity for each polygon for a color chosen from red, blue, green, red-edge, and infrared. The reference pixel color value (C_(ref)) for each field is then determined by averaging the darkest 20% of the mean values of pixel color intensity among all of the polygons in that field. Once the field's C_(ref) has been established, the Relative Color (RC) values of each pixel or polygon are obtained by dividing the value of the color (C_(i)) of each pixel or polygon by C_(ref). An estimated yield loss is then calculated using a correlation of yield loss as a function of RC that was predetermined using previously measured empirical data. Lastly, the yield loss (YL) values for each polygon are mapped onto the original aerial image coordinates, resulting in a yield loss map of the field. An economic analysis can then be provided as to whether to add nitrogen to the field or a portion thereof, based on the price of the crop, the amount of crop lost, and the cost of nitrogen fertilization.

In another aspect, within each polygon, a combination index value of each pixel is determined using at least two wavelengths, each chosen from about 400 nm to about 1 mm. In an aspect, the combination index value may be a Normalized Difference Vegetation Index. The reference index color value (I_(ref)) for each field is then determined by averaging the darkest about 10% to 20% of the combination index values among all of the polygons in that field. Once the field's I_(ref) has been established, the Relative Index (RI) values of each pixel or polygon are obtained by dividing the combination index value of each pixel or polygon by I_(ref). An estimated yield loss is then calculated using a correlation of yield loss as a function of RI that was predetermined using previously measured empirical data. Lastly, the YL values for each polygon are mapped onto the original aerial image coordinates, resulting in a yield loss map of the field. An economic analysis can then be provided as to whether to add nitrogen to the field or a portion thereof, based on the price of the crop, the amount of crop lost, and the cost of nitrogen fertilization.

Acquisition and Processing of High Resolution Images of Fields

Remote sensing data may be collected using a variety of instruments selected from the list comprising aircraft mounted camera, unmanned aerial vehicle (UAV) mounted camera, helicopter mounted camera, satellite-mounted camera, camera mounted on a tower or depressed area of the field, and combinations thereof. The altitude and camera focal length used to capture the field images are selected to capture the largest possible image of the field that is possible within the field of view of the camera, in order to maximize the resolution of the resulting image. For best results, the resolution of the resulting digital images falls in the range between about 0.01 m/pixel and about 30 m/pixel, between about 0.01 and about 0.1, between about 0.1 and 0.5, more preferably between about 0.2 and 2 m/pixel, and most preferably about 0.5 m/pixel. Alternatively, digital field images may be obtained from agricultural or meteorological databases operated by governmental or commercial entities. In an aspect, the crop may be corn, rice, wheat, potatoes, grass, or cotton. For cornfields, the aerial image of one or more fields of interest may be acquired when the crop is between the stages V8 to V18, and more preferably between the stages V10 to V18. Growth stage V8 occurs about 4 weeks after the emergence of the corn from the soil; the corn plant at stage V8 has grown to approximately 50% of its full height. Growth stage V18 occurs when the corn plant has grown to its full height and just before the plant enters into the reproductive stage.

Optionally, the aerial image may be cropped to include only the one or more fields of interest with field boundaries and eliminating areas of high soil exposure identified by the operator or using automated image-processing rules defined below. Image cropping may be performed either before or immediately following the spatial assignments. In many cases, it is preferable to crop the image to include only one field, or two adjacent fields, and repeat as needed to analyze all fields of interest. However, if there is insufficient information to determine C_(ref) or I_(ref) during image analysis, such as the absence of a pre-established reference area, or alternatively a sufficient number of fields lack the minimum number of nitrogen-sufficient regions to serve as reference areas, then cropping the image to include multiple fields may be preferable in order to establish a reliable estimate of C_(ref) or I_(ref).

Field boundaries are defined in the aerial photos using methods selected from the list comprising: using stored files such as shape files, that define previously established field boundaries to define the current field boundaries, or using an image analysis program to identify the field boundaries using a marking tool. Once the field boundaries are established, image pixels or polygons within the field boundaries are selected for analysis, and all other pixels falling outside the field boundaries are discarded. Many image-analysis programs, such as the Environment for Visualization of Images program (ENVI), possess tools to create image subsets, such as a Regions of Interest (ROI), based on the established field boundary lines.

The presence of bare soil in the aerial image may distort estimates of crop health and projected crop yield, so that the pixels corresponding to bare soil may be identified and removed using a number of techniques. A user may visually identify and manually remove the pixels corresponding to bare soil using existing image-processing software. Alternatively, the elimination of bare soil from the aerial image may be accomplished by discarding pixels in which the ratio of green/red color values falls within the ranges of values selected from the group comprising: a green/red color ratio of less than 1.1, or a green/red color ratio that is less than a green/red color ratio measured from bare soil in the same image when possible. In images that include near-infrared color values, the elimination of bare soil from the aerial image may be accomplished by discarding pixels with Normalized Difference Vegetation Indices that fall below a threshold value.

Assignment of Spatial Coordinates to Digital Field Images

Several well-established techniques are available to accomplish the spatial assignment of an aerial image. The spatial coordinates of an aerial image may be arbitrarily assigned based on the relative orientations between the pixels (or polygons) of the image, regardless their latitudes or longitudes. An aerial image of interest may be georeferenced to reflect the real world latitudes and longitudes of the image. Georeferencing may be accomplished during image acquisition, added to the image using reference points from standard images (Digital Ortho Quarter Quadrangles, example) or using landmarks in the image whose position is known or measured. Any of these techniques is acceptable so long as the accuracy of the spatial coordinates assigned is appropriate for the desired end use of the digital images. Once spatial coordinates are assigned to the digital image, each pixel or polygon will be associated with a unique value for location (latitude and longitude, or other alternative representations of location) and will additionally be associated with one or more values for color intensity.

Determination of C_(ref) and Calculation of Relative Color (RC)

The reference value of color corresponding to a section of field that is growing with ample available nitrogen (C_(ref)) is the benchmark for all color measurements, and all pixel measurements of color intensity are expressed as a fraction of the reference value of the color selected from blue, red, green, red-edge, and infrared. C_(ref) may be established by fertilizing a reference area of crop with a high rate of nitrogen early in the season, recording the area location, and identifying the area on the corresponding aerial image. C_(ref) may also be calculated as the average color value of all pixels or polygons contained in the reference area. Alternatively, the color values of all pixels or polygons in the one or more fields of interest may be sorted from low (dark color) to high (light color), and C_(ref) may be calculated as the mean or median color value of the pixels or polygons falling below the darkest 20% (lowest color values) of all pixels or polygons, or C_(ref) may be calculated as the mean or median color value of the pixels or polygons falling in the range between the darkest 10% and the darkest 20% of all pixels or polygons (lowest color values). Other methods could likely be used as long as a standard C_(ref) is established.

Thus, for each field, the relative value of color (Relative Color or RC) of each pixel or polygon in the one or more aerial images is calculated by dividing the value of green (C_(i)) of each pixel or polygon by C_(ref).

Determination of I_(ref) and Calculation of Relative Index Value (RI)

The reference index value corresponding to a section of field that is growing with ample available nitrogen (I_(ref)) is the benchmark for all combination index values. All combination index values at each pixel are expressed as a combination of at least two wavelengths present at each pixel In an aspect, the combination index value may be calculated by the following formula:

(WL1−WL2)/(WL1+WL2),

where WL1 is a first wavelength and WL2 is a second wavelength. The wavelengths may range from about 400 nm to about 1 mm. In an aspect, the color of the wavelengths may be selected from blue, red, green, red-edge, and infrared in any combination. In one aspect, WL1 is infrared and WL2 is selected from green, red, blue, or red-edge. I_(ref) may be calculated as the average combination index value of all pixels or polygons contained in the reference area. Alternatively, the combination index values of all pixels or polygons in the one or more fields of interest may be sorted from low to high, and I_(ref) may be calculated as the mean or median combination index value of the pixels or polygons falling below the darkest 20% (lowest color values) of all pixels or polygons, or I_(ref) may be calculated as the mean or median combination index value of the pixels or polygons falling in the range between the darkest 10% and the darkest 20% of all pixels or polygons. In another aspect, I_(ref) may be selected from the about 90^(th) percentile value of the sorted combination index values. Other methods could likely be used as long as a standard I_(ref) is established.

Thus, for each field, the relative index value (Relative Index or RI) of each pixel or polygon in the one or more aerial images is calculated by dividing the value of each combination index value (C_(i)) of each pixel or polygon by I_(ref).

Determination and Mapping of Yield Loss (YL)

The method described by the present invention is employed to predict crop yield losses due to nitrogen-deficiency stemming from causes such as low nitrogen fertilization rate with no mid-season loss of nitrogen (“nitrogen-stress-without-nitrogen-loss”), or sufficient nitrogen fertilization early in the season with subsequent nitrogen loss caused by wet weather or other factors (“nitrogen-loss”).

In an aspect, yield loss (YL) the predicted decrease in crop productivity (in bushels per acre) due to nitrogen deficiency, may be estimated as a function of Relative Color or Relative Index. In this aspect, the function may be a linear or nonlinear function.

In one aspect, yield loss may be calculated by substituting the Relative Color (RC) value or Relative Index (RI) value for each pixel or polygon of the Relative Color or Relative Index map into the linear relation:

YL=C ₁×RC−C ₂  Eqn. (1),

or

YL=C ₁×RI−C ₂  Eqn. (2),

where C₁ is the slope and C₂ is the intercept of a linear fit of measured corn yield data (see Examples 1, 3, 4, and 9), and both C₁ and C₂ assume different values depending on a variety of factors including, but not limited to: the cause of the nitrogen-deficiency, the particular crop species, the color or colors used to develop the Relative Color or Relative Index Map. In various aspects, C₁ and C₂ for estimating yield loss using RC or RI may range from about 75 to about 700, from about 75 to about 150, from about 100 to about 500, and from about 150 to about 700. For example, if leaching or denitrification in the soil causes the nitrogen-deficiency (“nitrogen-loss”) and the color is green, C₁ may be set to be approximately equal to C₂ and both C₁ and C₂ may range between about 75 and about 100, and more preferably between about 85 and about 90. In another example, for the case of nitrogen-deficiency caused by low initial nitrogen-fertilization rates (“nitrogen-stress-without-nitrogen-loss”) and the selected color is green, the difference between C₁ and C₂ of the aforesaid equation may be about 20, C₁ may range between about 120 and about 700, and C₂ may range between about 110 and about 700.

Yield losses may be calculated for the areas represented by pixels, as well as or for larger areas created by aggregating pixels into polygons. In the latter case, the yield loss of each polygon may be calculated by substituting the average of the RC or RI values of all pixels within the polygon into Eqn. 1 or Eqn. 2.

Yield losses for each pixel or polygon are mapped onto the aerial image using the paired yield loss and spatial location values stored for each pixel. The resulting yield loss map helps the producer determine the predicted yield of the fields, and the location of any rescue nitrogen-fertilizations that may be required.

Determination and Mapping of Economically Optimal Nitrogen Fertilization Rate

In the case of low initial nitrogen fertilizer rate (“nitrogen-stress-without-nitrogen-loss”), an economically optimal nitrogen rate (EONR) may be calculated by substituting the RC or RI value for the pixel or polygon into the following linear transformations:

EONR=C ₃×RC−C ₄  (Eqn. 3),

or

EONR=C ₃×RI−C ₄  (Eqn. 4),

where C₃ is the slope and C₄ is the intercept of a linear fit of empirical data, using a method similar to the method used to determine the values of C₁ and C₂ (see Example 1). In various aspects, C₃ and C₄ for estimating EONR using RC or RI may range from about 75 to about 700, from about 75 to about 150, from about 100 to about 500, and from about 150 to about 700. For example, if the selected color is green, the value of C₃ may be set to be higher than C₄ by a difference ranging between about 20 and about 60 in an aspect. In this aspect, the value of C₃ may range between about 300 and about 400, and the value of C₄ may range between about 250 and about 350. The empirical data used to establish the linear transformation in this aspect were collected from 23 small plot experiments in farmer fields in Missouri.

In addition, the EONR and spatial location data stored with each pixel or polygon may be used to construct an EONR map to provide a producer or other user with information on an estimated minimum amount of nitrogen fertilizer to use in the midseason application in order to minimize the predicted yield losses and recover the revenue that would have otherwise been lost due to a decrease in overall crop yield. Thus, the precise amount of additional nitrogen fertilizer needed to realize the maximum potential crop yield may be determined from the EONR map.

The information contained in the yield loss map and the information contained in the EONR map may be combined to facilitate the management of nitrogen fertilizer. The total cost of additional nitrogen fertilization may be easily determined because the exact amount and location of fertilizer application is provided. Given additional information about the value of the crop, the economic loss incurred by yield loss if additional nitrogen fertilizer is not provided may also be determined. If the potential increase in the value of the harvest exceeds the expense of additional nitrogen fertilization, the producer would realize a net economic gain by fertilizing. In addition, because the information is provided as spatially mapped information, the producer is provided with the necessary information to perform a similar economic analysis on subsets or sub-regions of the crop field.

It should be understood from the foregoing that, while particular embodiments have been illustrated and described, various modifications can be made thereto without departing from the spirit and scope of the invention as will be apparent to those skilled in the art. Such changes and modifications are within the scope and teachings of this invention as defined in the claims appended hereto.

EXAMPLES

The following examples illustrate the invention.

Example 1 Development of Method to Estimate Yield Losses from Aerial Photographs

To develop and test a method to estimate corn yield loss due to nitrogen deficiency, the following experiment was conducted. Based on the hypothesis that the areas of cornfields experiencing higher nitrogen loss would appear lighter in aerial photographs and produce lower yields, aerial photographs of seven cornfields that had received above-average May and June rainfall were analyzed as described below.

Selection and characteristics of experimental fields: Seven study fields were located in four counties in the northern half of Missouri, spread over a distance of 270 km, and represented a moderate range of geographies, landscape positions, soil genesis factors, and surface soil textures (see Table 1). All seven fields had uniform fertilization histories. All fields were located in regions that received higher-than average precipitation in May and June, and therefore had a high potential for nitrogen losses due to leaching and denitrification losses. The fields used in this experiment were selected based on the determination of potential nitrogen deficiency by cooperating producers.

TABLE 1 Information on seven production cornfields photographed in 2001 and 2004. Surface Photo Polygon Soil great soil resolution Area size Polygon Field Year Soil region group texture (m/pixel) (ha) (m²) count AL1 2004 Alluvial Hapludolls* Silty 2.00 41.8 16 13899 clay AL2 2004 Alluvial Endoaquerts* Clay 2.00 27.0 16 9686 AL3 2001 Alluvial Endoaquolls* Silty 1.00 2.3 9 1562 clay CP1 2001 Claypan Epiaqualfs Silty 0.54 7.4 10 5421 loam CP2 2001 Claypan Albaqualfs Silty 0.56 6.3 21 1468 loam CP3 2001 Claypan Epiaqualfs Silty 0.42 8.7 21 2103 loam CP4 2001 Claypan Epiaqualfs Silty 0.42 5.6 21 1401 loam *All three alluvial fields contained map units representing more than one great group. The primary great group was listed and made up between 60% and 70% of the field area. Secondary great groups, by field, were: AL1, Endoaquerts; AL2, Hapludolls; AL3, Udifluvents.

Aerial photograph acquisition, digitization, and rectification: Aerial photographic images were acquired from five production cornfields in 2001 and two production cornfields in 2004. Aerial photographs in 2001 were taken from small-plane flyovers in a nadir (straight down) orientation at altitudes ranging from 1000-1400 m above ground level using ASA 400 35 mm color positive film. Larger fields were photographed from higher altitudes to fit the whole field onto the camera's field of view. Photos were obtained on 5 Jul. 2001, and the growth stage of the corn at that time was approximately V11 to V13. The film was processed into color slides, and then digitized using a Nikon CoolScan 1.05 film scanner (Nikon, Inc., Melville, N.Y.). The spatial resolution of the digitized images ranged from 0.42 to 1.00 m per pixel (see Table 1), depending on differences in the altitudes at which the aerial photographs were obtained and differences in the focal length used by the camera to obtain the aerial photographs. Using the Environment for Visualizing Images (ENVI) software version 3.5 (Research Systems, Inc., Boulder, Colo.), the aerial photos were rectified and formatted to the Universal Transverse Mercator coordinate system that incorporated the North American Datum of 1983 (NAD83), using coordinate points collected from Digital Ortho Quarter Quads produced by the U.S. Geological Survey and obtained from the map room of the Center for Agricultural, Resource, and Environmental Systems (http://cares.missouri.edu/index.asp). Georeferenced digital aerial photographic images for the two additional fields, acquired on 24 Jun. 2004 at an estimated corn growth stage of V10 to V11, were obtained from the National Agricultural Imaging Program (Farm Service Agency, U.S. Dept. of Agriculture). These additional aerial images had a spatial resolution of 2 m per pixel with 10 m stated accuracy.

Yield monitor data associated with image data: Maps of corn grain yield were obtained from the producers and processed using Spatial Management System Basic (Ag Leader Technology, Inc., Ames, Iowa). The location of each reported corn grain yield was used as the centroid for a rectangular polygon in the rectified aerial photographic images. “Closed” blanking (BLN) files, containing the coordinates of the vertices of the closed rectangular polygons, were constructed using Microsoft Excel (Microsoft Corp., Redmond, Wash.), imported as text files into Surfer 7.0 (Golden Software, Inc., Golden, Colo.), exported as shapefiles into ENVI 3.5, and used as Regions of Interest in the rectified images. The Regions of Interest were used to extract and export mean digital counts (DCs) for red, green, and blue wavelengths, as well as the associated geographic map coordinates for each polygon. Yield data and mean red, green, and blue DCs for each polygon were merged using SAS version 8.2 (SAS Institute, Cary, N.C.).

Aerial image processing: Several photographs contained areas of low vegetative cover, which were removed from the analysis to reduce errors in the appearance of the crop. All polygons with a green/red pixel color ratio of less than 1.2 were removed from the analysis, using a decision rule developed using previously acquired photographs of corn fields with high resolution (˜4 cm) and low vegetative cover. Using this procedure, no polygons were eliminated from the A3 and CP2 fields. The CP3 and CP4 fields had 15% and 55% of the polygons removed, respectively, which were in areas identified by the cooperating corn producer as having severe black cutworm [Agrotis ipsilon (Hufnagel)] damage. The A1 and A2 fields had 17% and 15% of the polygons removed, respectively, mainly in areas identified by the cooperating corn producer as drainage channels. The CP1 field had 23% of the polygons removed, mainly at one end of the field that was identified by producers as suffering substantial stand loss due to excess rainfall and subsequent seedling disease.

Aerial photographic image data processing: The post-processing of the digitized aerial photographs focused on the green pixel values relative to a reference green value, based on previous research that indicated that the plant's nitrogen status was more closely related to green reflectance than to red or blue reflectance, and additional previous research that suggested that relative color from aerial imagery was a more accurate and reliable indicator of nitrogen status than absolute color. The reference green DC (G_(ref)) for each field's photographic image was set equal to the mean green DC from the darkest (lowest green DC) 20% of polygons, and represented those areas with sufficient availability of nitrogen, and the relative green (RG) value for each polygon was then calculated as the green DC for each polygon divided by the reference green DC.

In order to compare color-yield relationships across multiple fields, a reference yield value for each field was used to normalize the expression of yield. Reference yield was defined as the average yield for the same polygons (i.e. the darkest 20%) used in establishing the reference green value. The relative yield for each polygon was calculated by dividing each polygon's yield by the reference yield, and yield loss was calculated by subtracting the reported yield for each polygon from the reference yield.

Polygons in each digitized aerial image were grouped by relative green value into classes with a constant interval of relative green value (<1.00, 1.01 to 1.05, 1.06 to 1.10, 1.11 to 1.15, 1.16 to 1.20, etc.). All data associated with each polygon were aggregated into each of the classes, and mean values for relative green, relative yield, and yield losses were calculated for each class. Class means for relative yield and yield loss were regressed against class means for relative green using SAS software version 8.2 (SAS Institute, Cary, N.C.).

Relationship between aerial photographic data and crop yield: In each of the seven study fields, relative yield decreased significantly (P<0.002 in each field) as relative green increased, shown in FIG. 2. This observation was consistent with the hypothesis that lighter areas (with higher green DC and relative green values) had experienced nitrogen loss, which subsequently limited corn yield. The strength of the relationship was related to the degree of nitrogen stress, as assessed by the observed range of either relative green or relative yield. Coefficient of determination ranged from 0.62 in the field with the least nitrogen stress to >0.9 in the three fields with the most nitrogen stress. Within each relative green class, there was often considerable variability in relative yield that could be attributed to other landscape and management factors. In aggregate, however, this variability did not mask the effects of nitrogen on yield potential, suggesting that nitrogen was a major factor limiting yields in these fields. The relationship between relative green and relative yield was similar among all fields, though the CP1 and CP4 fields had steeper slopes than other fields (P=0.011 and 0.0005, respectively, using a test for equality of slope between individual locations vs. all locations combined). The observed similarities between fields suggested that a general relationship, shown in FIG. 3, could be used to predict relative yield from future aerial photographs with reasonable accuracy and reliability (r₂=0.79).

Relative greenness was also related to yield loss in each study field, and summarized in FIG. 4 (P<0.002 in each field except CP3, where P=0.12). As with relative yield, coefficient of determination was lowest in the field with the least nitrogen stress and highest in the fields with the most nitrogen stress. The similarity of this relationship across fields was even more striking than for the relationship between relative greenness and relative yield. When data from all fields were combined to form a general relationship, as shown in FIG. 5, the coefficient of determination was 0.91, which suggested that potential yield loss can be estimated with good accuracy from aerial photographs for cases of nitrogen loss.

When data were standardized to reference values for each field and combined, relative green predicted relative yield with r₂=0.79 and yield loss with r₂=0.91. Aerial photos provided reasonable predictions of yield loss due to nitrogen deficiency. These predictions may help corn producers decide how much expense and trouble is justified in making rescue nitrogen applications, and additionally may permit large-scale evaluation of the susceptibility of different nitrogen fertilizer management strategies to address nitrogen loss.

Example 2 Aerial Photo Data Used to Manage Nitrogen Supplementation

To demonstrate the feasibility of using aerial photo data to assess crop health and to determine the appropriate rates of nitrogen supplementation, a demonstration project was established in 2006. This project used data obtained from aerial photos using the methods described in Example 1 to guide nitrogen fertilizer application through a center-pivot irrigation system, as illustrated in FIG. 6. In this demonstration project, the normal pre-planting nitrogen application was reduced by 50%, and aerial photographs were used to diagnose the additional nitrogen application rate needed for 150 pivot-irrigated acres. Based on the fertilization rate determined by the methods described in Example 1, nitrogen fertilizer use was reduced by 8500 lb of nitrogen (28,000 lb nitrogen fertilizer solution), or 28% of the normal nitrogen application rate. This recommended nitrogen fertilization rate resulted in a modest 84 bu loss in corn yield, or 0.25% of the field's total yield. Results from the south field of this demonstration project are shown in FIG. 6.

Example 3 Nitrogen Management Methods Using Aerial Photo Data May be Used to Manage Nitrogen Fertilization Rates on Experimental Survey Areas

To refine the relationship between aerial photo data and corn yield loss developed using the methods described in Example 1, three experimental survey areas of 1200 to 2000 acres were established in the Missouri River bottom of Holt County, Missouri, which received excessive rainfall in April and May 2005. Based on the predictive relationship developed in Example 1, aerial photographs were used to predict an average of 25 bu/acre lost yield potential over the survey areas due to nitrogen deficiency. Extrapolated over the whole Missouri River bottom in Holt County, this amounted to 1.8 million bushels of lost corn yield in 2005, or about $3.6 million of lost income. Working with community agronomists and individual producers to collect nitrogen fertilizer management information for these fields, different nitrogen fertilizer sources and multiple application methods may be compared to determine which strategies are most successful at preventing nitrogen loss.

Example 4 Estimating Yield Losses Using Relative Blue Measurements from Aerial Photographs

Using the methods described in Example 1, a correlation between Yield Loss and Relative Blue values as measured from aerial photographs of six crop fields was developed. FIG. 7 is a summary of the correlation, which had a C1 of 154.01 and a C2 of 153.03. The results of this experiment demonstrated the feasibility of estimating Yield Loss using Relative Blue values as the Relative Color measurement from the aerial photographs of crop field.

Example 5 Estimating Yield Losses Using Relative Red Measurements from Aerial Photographs

Using the methods described in Example 1, a correlation between Yield Loss and Relative Red values as measured from aerial photographs of six crop fields was developed. FIG. 8 is a summary of the correlation, which had a C1 of 136.24 and a C2 of 136.38. The results of this experiment demonstrated the feasibility of estimating Yield Loss using Relative Red values as the Relative Color measurement from the aerial photographs of crop field.

Example 6 Estimating Yield Losses Using Relative Index Measurements from Aerial Photographs

Using the methods described in Example 1, a correlation between Yield Loss and Relative Index values as measured from aerial photographs of crop fields was developed. FIG. 9 is a summary of the correlation, which had a C1 of 146.12 and a C2 of 149.58. In general, for each pixel, the combination index value was calculated using the formula: (infrared−green)/(infrared+green). All of the combination index values were sorted in the field and the 90^(th) percentile value was set as the reference index value. For each pixel, the Relative Index value was calculated as Relative Index=combination index value for each pixel divided by the reference index value. A mathematical relationship was applied, such as the one shown in the graph of FIG. 9, to predict yield loss. The results of this experiment demonstrated the feasibility of estimating Yield Loss using Relative Index values as the measurement from the aerial photographs of crop field. 

We claim:
 1. A method for determining a crop yield loss due to nitrogen deficiency in at least one or more crop fields based on an analysis of at least one or more remote sensing images, the method comprising: a. obtaining the one or more remote sensing images of the at least one or more crop fields; b. assigning spatial coordinates to the at least one or more remote sensing images, represented by pixels or polygons comprised of aggregated pixels, from the at least one or more remote sensing images; c. calculating a combination index value comprising at least two wavelengths at each pixel; d. selecting a reference index value from the combination index values; e. calculating a relative index value of each pixel in the at least one or more remote sensing images by dividing the combination index value by the reference index value; f. estimating a yield loss of each pixel from a function of the relative index values; and, g. constructing a yield loss map from a spatially referenced yield loss of each pixel; wherein the yield loss comprises a decrease in crop yield per acre of a crop.
 2. The method of claim 1, wherein the yield loss (YL) of each pixel is estimated by substituting the relative index value (RI) of each pixel into the formula YL=C₁×RI−C₂, wherein C₁ and C₂ are empirically derived constants.
 3. The method of claim 2, wherein C₁ is set to a value ranging between about 75 and about 700 and C2 is set to a value ranging between about 75 and about
 700. 4. The method of claim 1, wherein the at least two wavelengths range from about 400 nm to about 1 mm.
 5. The method of claim 1, wherein the combination index value at each pixel comprises a first wavelength (WL1) and a second wavelength (WL2) and is calculated by the formula (WL1−WL2)/(WL1+WL2).
 6. The method of claim 1, further comprising sorting the combination index values in the at least one or more remote sensing images prior to selecting a reference index value.
 7. The method of claim 6, wherein the reference index value is selected from the about 90^(th) percentile value of the sorted combination index values.
 8. The method of claim 1, wherein the reference index value for each remote sensing image is established as a constant value selected from: a mean or a median combination index value of the pixels falling in an area of a field with ample nitrogen availability; a mean or a median combination index value of a darkest 20% of all pixels in an entire field; a mean or a median combination index value of the pixels or polygons falling between a darkest 10% and the darkest 20% of all pixels in the entire field; or a mean or a median combination index value of the pixels or polygons in the portion of the field that is judged to be nitrogen-sufficient.
 9. The method of claim 1, wherein the crop is selected from the group comprising corn, rice, wheat, potatoes, grass, and cotton.
 10. The method of claim 1, wherein the at least one or more remote sensing images is a digital image with a resolution ranging between about 0.01 meters per pixel and about 30 meters per pixel, wherein the digital image is chosen from aerial photographs, satellite photographs, photographs obtained by drones, and photographs obtained by tower mounted cameras.
 11. The method of claim 1, further comprising h. determining a cost of nitrogen fertilization of the crop at a recommended nitrogen application rate and a projected value of the yield loss of the crop; and, i. applying nitrogen fertilizer at the recommended nitrogen application rate if the projected value of the yield loss of the crop exceeds the cost of nitrogen fertilization by at least 20%.
 12. A method of determining a nitrogen fertilization rate of a crop field at mid-season to ameliorate nitrogen deficiency using a spatially referenced map of relative index values (RI), wherein each RI comprises a combination index value at a location in a canopy of the crop field relative to a reference index value, the method comprising: a. estimating an economically optimal nitrogen rate (EONR) corresponding to each RG of the spatially referenced map by substituting each RI into the equation EONR=C ₃×RI−C ₄ wherein C₃ and C₄ are empirically derived constants; and b. mapping each EONR corresponding to each RI onto a spatially referenced EONR map; wherein each EONR comprises a recommended amount of nitrogen per unit area to be applied at mid-season in order to minimize a predicted crop yield loss due to nitrogen deficiency.
 13. The method of claim 12, wherein each EONR comprises a recommended amount of nitrogen per unit area to be applied at mid-season in order to maximize a predicted potential crop yield.
 14. The method of claim 12, wherein C₃ is set to a value ranging between about 75 and about 700 and C₄ is set to a value ranging between about 75 and about
 700. 15. A method for determining a crop yield loss due to nitrogen deficiency in at least one or more crop fields based on an analysis of at least one or more remote sensing images, the method comprising: a. obtaining the one or more remote sensing images of the at least one or more crop fields; b. assigning spatial coordinates to the at least one or more remote sensing images, represented by pixels or polygons comprised of aggregated pixels, from the at least one or more remote sensing images; c. establishing a reference color value for a reflectivity of a color for the at least one or more remote sensing images, wherein the color is selected from red, blue, green, red-edge, and infrared; d. calculating a relative color value of each pixel in the at least one or more remote sensing images by dividing a color value of each pixel by the reference color value; e. estimating a yield loss of each pixel from a function of the relative index values; and, f. constructing a yield loss map from a spatially referenced yield loss of each pixel; wherein the yield loss comprises a decrease in crop yield per acre of a crop.
 16. The method of claim 15, wherein the yield loss (YL) of each pixel is estimated by substituting the relative color value (RC) of each pixel into the formula YL=C₁×RC−C₂.
 17. The method of claim 16, wherein C₁ and C₂ are empirically derived constants each set to a value ranging from about 75 to about
 700. 18. A method of determining the yield loss of a crop due to nitrogen deficiency based on a spatially referenced map comprising a plurality of spatial coordinates and corresponding relative color values within in a crop field, the method comprising: a. estimating the yield loss of each spatial coordinate of the spatially referenced map; and, b. constructing a yield loss map from a spatially referenced YL of each spatial coordinate; wherein the yield loss comprises a decrease in crop yield per acre of a crop.
 19. The method of claim 18, wherein the yield loss (YL) of each spatial coordinate of the spatially referenced map is estimated by substituting each corresponding relative color value (RC) into the formula YL=C₁×RC−C₂, in which C₁ and C₂ are empirically-derived constants each set to a value ranging from about 75 to about
 700. 